{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RGILDVMW7LF4QTFFG4JN2BFDW4","short_pith_number":"pith:RGILDVMW","canonical_record":{"source":{"id":"1809.02758","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-08T05:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"8778bf197389e8a0ac4317f29c64e24d8082a2baa642f75720dd1483f7ba4e3e","abstract_canon_sha256":"6eef53a7546d01892938d270ae6facb8c98d8c735c4cbfdd0f4cdb7a53638a13"},"schema_version":"1.0"},"canonical_sha256":"8990b1d596facbc84ca53712dd04a3b735b1c5cb2341b4afb7e4e7b62c440788","source":{"kind":"arxiv","id":"1809.02758","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02758","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02758v1","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02758","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"RGILDVMW7LF4","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RGILDVMW7LF4QTFF","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RGILDVMW","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RGILDVMW7LF4QTFFG4JN2BFDW4","target":"record","payload":{"canonical_record":{"source":{"id":"1809.02758","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-08T05:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"8778bf197389e8a0ac4317f29c64e24d8082a2baa642f75720dd1483f7ba4e3e","abstract_canon_sha256":"6eef53a7546d01892938d270ae6facb8c98d8c735c4cbfdd0f4cdb7a53638a13"},"schema_version":"1.0"},"canonical_sha256":"8990b1d596facbc84ca53712dd04a3b735b1c5cb2341b4afb7e4e7b62c440788","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:15.383920Z","signature_b64":"K+ngSmQnb1ej6CQ3WuMvWH573Pp+ecxlZ5kIIT0a1nxS1JM51vCiHThAU+wD9BtQJC9GUE16Rentsl2tjvkQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8990b1d596facbc84ca53712dd04a3b735b1c5cb2341b4afb7e4e7b62c440788","last_reissued_at":"2026-05-18T00:06:15.383419Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:15.383419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.02758","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gH0/lyYJX56gYzep20AiZtmIQRSmrnEbTScdMYCOAf7falfdChuIXjRMhuzWDCEoj0Q5tgJehAsJPUA2xewWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:54:21.124894Z"},"content_sha256":"5c2b94b6ea7df2c2f180216df57a661186ca1254b9445407df151f42bb0a5a4f","schema_version":"1.0","event_id":"sha256:5c2b94b6ea7df2c2f180216df57a661186ca1254b9445407df151f42bb0a5a4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RGILDVMW7LF4QTFFG4JN2BFDW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Translation surfaces in Euclidean space with constant Gaussian curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Rafael L\\'opez, Thomas Hasanis","submitted_at":"2018-09-08T05:01:43Z","abstract_excerpt":"We prove that the only surfaces in $3$-dimensional Euclidean space $\\R^3$ with constant Gaussian curvature $K$ and constructed by the sum of two space curves are cylindrical surfaces, in particular, $K=0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02758","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LgXixTxNae2GDxwZMm5AreFGwFD34VJKILYiXTtP1iPEVF4atTZmH6+bined6yzJ0l0NTC5tdZveM/+Mcm+kBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:54:21.125227Z"},"content_sha256":"ae04636358f7c4f3f9b2aacb19386152881519a25a26101d7c3b3f9cbb38ade1","schema_version":"1.0","event_id":"sha256:ae04636358f7c4f3f9b2aacb19386152881519a25a26101d7c3b3f9cbb38ade1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RGILDVMW7LF4QTFFG4JN2BFDW4/bundle.json","state_url":"https://pith.science/pith/RGILDVMW7LF4QTFFG4JN2BFDW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RGILDVMW7LF4QTFFG4JN2BFDW4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T05:54:21Z","links":{"resolver":"https://pith.science/pith/RGILDVMW7LF4QTFFG4JN2BFDW4","bundle":"https://pith.science/pith/RGILDVMW7LF4QTFFG4JN2BFDW4/bundle.json","state":"https://pith.science/pith/RGILDVMW7LF4QTFFG4JN2BFDW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RGILDVMW7LF4QTFFG4JN2BFDW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RGILDVMW7LF4QTFFG4JN2BFDW4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6eef53a7546d01892938d270ae6facb8c98d8c735c4cbfdd0f4cdb7a53638a13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-08T05:01:43Z","title_canon_sha256":"8778bf197389e8a0ac4317f29c64e24d8082a2baa642f75720dd1483f7ba4e3e"},"schema_version":"1.0","source":{"id":"1809.02758","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02758","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02758v1","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02758","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"RGILDVMW7LF4","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RGILDVMW7LF4QTFF","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RGILDVMW","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:ae04636358f7c4f3f9b2aacb19386152881519a25a26101d7c3b3f9cbb38ade1","target":"graph","created_at":"2026-05-18T00:06:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that the only surfaces in $3$-dimensional Euclidean space $\\R^3$ with constant Gaussian curvature $K$ and constructed by the sum of two space curves are cylindrical surfaces, in particular, $K=0$.","authors_text":"Rafael L\\'opez, Thomas Hasanis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-08T05:01:43Z","title":"Translation surfaces in Euclidean space with constant Gaussian curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02758","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5c2b94b6ea7df2c2f180216df57a661186ca1254b9445407df151f42bb0a5a4f","target":"record","created_at":"2026-05-18T00:06:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6eef53a7546d01892938d270ae6facb8c98d8c735c4cbfdd0f4cdb7a53638a13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-08T05:01:43Z","title_canon_sha256":"8778bf197389e8a0ac4317f29c64e24d8082a2baa642f75720dd1483f7ba4e3e"},"schema_version":"1.0","source":{"id":"1809.02758","kind":"arxiv","version":1}},"canonical_sha256":"8990b1d596facbc84ca53712dd04a3b735b1c5cb2341b4afb7e4e7b62c440788","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8990b1d596facbc84ca53712dd04a3b735b1c5cb2341b4afb7e4e7b62c440788","first_computed_at":"2026-05-18T00:06:15.383419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:15.383419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K+ngSmQnb1ej6CQ3WuMvWH573Pp+ecxlZ5kIIT0a1nxS1JM51vCiHThAU+wD9BtQJC9GUE16Rentsl2tjvkQBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:15.383920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02758","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c2b94b6ea7df2c2f180216df57a661186ca1254b9445407df151f42bb0a5a4f","sha256:ae04636358f7c4f3f9b2aacb19386152881519a25a26101d7c3b3f9cbb38ade1"],"state_sha256":"223d8e5dac530add66d1d46679e09c747bb2bcbd4ea231e7485f32fc52702e65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TvX9YffUUzZs9343E37HKm3L9kVMxhQLtwZaBajt8k3zpWvzcmzfgMAvwazqsieLUIh0LHYgAPoZfWulcZpLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:54:21.127159Z","bundle_sha256":"eae6f3b40bb4ea6272d577e6f9bd7b87818bcfcaa60adc18e82c029f2b3b1d4d"}}